Question

(1 point) Rework problem 18 from section 3.3 of your text, involving filling in missing probabilities on a tree diagram. Construct a copy of figure 3.11 in your text, where the first outcome is one of (A,B,C) and the second outcome in each case is one of (1,2,3) (only 1 or 2 in the case of outcome C). Use the following probabilities instead of those given in your text: 12 12 12 12 Find the following missing probabilities (1) Pr[A (3) Pr[2|A]- (4) Pr[B] - (5) Pr(I|B] = (6) Pr3)B (7) Pr[B2]- (9) Pr[1C1- (10) Pr[21C]-

Answer 1

1) P(A) = P(A1) + P(A2) + P(A3) = 1/12 + 1/12 + 1/12 = 3/12 = 1/4

2) P(1 | A) = P(A1) / P(A) = (1/12) / (1/4) = 1/3

3) P(2 | A) = 1/3

4) P(B) = 1 - [P(A) + P(C)] = 1 - [P(A) + P(C1) + P(C2)] = 1 - (1/4 + 1/6 + 1/12) = 1/2

5) P(1 | B) = P(B1) / P(B) = (1/6) / (1/2) = 1/3

6) P(3 | B) = P(B3) / P(B) = (1/4) / (1/2) = 1/2

7) P(B2) = P(2 | B)*P(B) = (1/6)*(1/2) = 1/12

8) P(C) = P(C1) + P(C2) = 1/6 + 1/12 = 1/4

9) P(1 | C) = P(C1) / P(C) = (1/6) / (1/4) = 2/3

10) P(2 | C) = P(C2) / P(C) = (1/12) / (1/4) = 1/3